Please Explain 0C0 = 1 (1 Viewer)

[mercury]

nCr = n!/r!(n-r)!

This can be derived from the definition of permutation and combinations. Now there is also a direct correlation between Pascal's triangle and combinations.
1
1 1
1 2 1
1 3 3 1

0C0
1C0 1C0
2C0 2C1 2C0
3C0 3C1 3C1 3C0

However 0C0 = 0!/0!0! Having known that n/0 is undefined, how is it 0C0 = 1? Choosing nothing from nothing...!

EDIT:

0! =1 by definition, I guess this explains why the expression is not undefined.
It's all good!

If you want to know why it is so by definition, go to:

Why does 0! = 1 ?

 

[Fosweb]

Originally posted by mercury
Choosing nothing from nothing...

You said it right there. Only one way you can do this...

But this definition 'just has to be', for all others to work. Mathematicians have made up lots of stuff so other stuff can 'just work'...

 

[jogloran]

My teacher said that you can think of it as due to the fact that there's only one way to choose nothing from ... nothing...